Power Estimation in Multivariate Analysis of Variance

Power is often overlooked in designing multivariate studies for the simple reason that it is believed to be too complicated. In this paper, it is shown that power estimation in multivariate analysis of variance (MANOVA) can be approximated using a F distribution for the three popular statistics (Hotelling-Lawley trace, Pillai-Bartlett trace, Wilk`s likelihood ratio). Consequently, the same procedure, as in any statistical test, can be used: computation of the critical F value, computation of the noncentral parameter (as a function of the effect size) and finally estimation of power using a noncentral F distribution. Various numerical examples are provided which help to understand and to apply the method. Problems related to post hoc power estimation are discussed.